Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s3973" xml:space="preserve">
              <pb file="0160" n="160" rhead="FED. COMMANDINI"/>
            æqualibus baſibus, quorum axes cum baſibus æquales an
              <lb/>
            gulos faciant. </s>
            <s xml:id="echoid-s3974" xml:space="preserve">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
              <lb/>
            e f ad axem g h: </s>
            <s xml:id="echoid-s3975" xml:space="preserve">nam ſi axes ad planum baſis recti ſint, il-
              <lb/>
            lud perſpicue conſtat: </s>
            <s xml:id="echoid-s3976" xml:space="preserve">quoniam eadem linea, & </s>
            <s xml:id="echoid-s3977" xml:space="preserve">axem & </s>
            <s xml:id="echoid-s3978" xml:space="preserve">ſoli
              <lb/>
            di altitudinem determinabit. </s>
            <s xml:id="echoid-s3979" xml:space="preserve">Si uero ſintinclinati, à pun-
              <lb/>
            ctis e g ad ſubiectum planum perpendiculares ducantur
              <lb/>
            e k, g l: </s>
            <s xml:id="echoid-s3980" xml:space="preserve">& </s>
            <s xml:id="echoid-s3981" xml:space="preserve">iungantur f_k_, h l. </s>
            <s xml:id="echoid-s3982" xml:space="preserve">rurſus quoniam axes cum ba
              <lb/>
            ſibus æquales faciunt angulos, eodem modo demonſtrabi
              <lb/>
            tur, triangulum e f K triangulo g h l ſimile eſſe: </s>
            <s xml:id="echoid-s3983" xml:space="preserve">& </s>
            <s xml:id="echoid-s3984" xml:space="preserve">e k ad g l,
              <lb/>
            ut e f ad g h. </s>
            <s xml:id="echoid-s3985" xml:space="preserve">Solidum autem a b ad ſolidum c d eſt, ut
              <lb/>
            e K ad g l. </s>
            <s xml:id="echoid-s3986" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3987" xml:space="preserve">ut axis e f ad axem g h. </s>
            <s xml:id="echoid-s3988" xml:space="preserve">quæ omnia de
              <lb/>
            monſtrare oportebat.</s>
            <s xml:id="echoid-s3989" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3990" xml:space="preserve">Ex iis quæ demonſtrata ſunt, facile conſtare
              <lb/>
            poteſt, priſmata omnia & </s>
            <s xml:id="echoid-s3991" xml:space="preserve">pyramides, quæ trian-
              <lb/>
            gulares baſes habent, ſiue in eiſdem, ſiue in æqua
              <lb/>
            libus baſibus conſtituantur, eandem proportio-
              <lb/>
              <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">15. quinti</note>
            nem habere, quam altitudines: </s>
            <s xml:id="echoid-s3992" xml:space="preserve">& </s>
            <s xml:id="echoid-s3993" xml:space="preserve">ſi axes cum ba
              <lb/>
            ſibus æquales angulos contineant, ſimiliter ean-
              <lb/>
            dem, quam axes, habere proportionem: </s>
            <s xml:id="echoid-s3994" xml:space="preserve">ſunt
              <lb/>
              <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">28. unde-
                <lb/>
              cimi.</note>
            enim ſolida parallelepipeda priſmatum triangula
              <lb/>
            res baſes habentiũ dupla; </s>
            <s xml:id="echoid-s3995" xml:space="preserve">& </s>
            <s xml:id="echoid-s3996" xml:space="preserve">pyramidum ſextupla.</s>
            <s xml:id="echoid-s3997" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">7. duode-
            <lb/>
          cimi.</note>
        </div>
        <div xml:id="echoid-div247" type="section" level="1" n="85">
          <head xml:id="echoid-head92" xml:space="preserve">THE OREMA XVI. PROPOSITIO XX.</head>
          <p>
            <s xml:id="echoid-s3998" xml:space="preserve">Priſmata omnia & </s>
            <s xml:id="echoid-s3999" xml:space="preserve">pyramides, quæ in eiſdem,
              <lb/>
            uel æqualibus baſibus conſtituuntur, eam inter
              <lb/>
            ſe proportionem habent, quam altitudines: </s>
            <s xml:id="echoid-s4000" xml:space="preserve">& </s>
            <s xml:id="echoid-s4001" xml:space="preserve">ſi
              <lb/>
            axes cum baſibus faciant angulos æquales, eam
              <lb/>
            etiam, quam axes habent proportionem.</s>
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